In the last year’s we’ve witnessed a renaissance in network theory, with the introduction of hypergraphs to model systems beyond pairwise interactions. The community started the endeavour of translating already known graph-based measures to this new setting. A key bridge between graph theory and complex networks is that of spectral centrality measures (e.g. eigenvector, PageRank, …). In hypergraphs, where the adjacency tensor(s) are involved, this is technically challenging. Still, Benson [1] managed to give three sensible extensions to this problem, although under very limiting assumptions: uniformity in the hyperedges (same number of nodes per interaction) and undirectedness. In this talk we first review the basics of what a centrality is, in standard networks, focusing particularly in the spectral ones, as well as some basic notions of hypergraphs. We then discuss how can we move beyond the first limitation [2] and possibly address the spectral centrality of other higher order structures as well. [1] Three Hypergraph Eigenvector Centralities, A. R. Benson, SIAM Mathematics of Data Science (2019) [2] Uplifting edges in higher order networks: spectral centralities for non-uniform hypergraphs, G. Contreras-Aso, C. Pérez-Corral, M. Romance, arXiv:2310.20335 (2023), under review at SIAM Mathematics of Data Science.
In this discussion, I want to focus on the nuances of peer review within interdisciplinary research, particularly from the viewpoint of early-career scientists. I will share my experience of the reviewing process and then follow it with an open discussion where we propose strategies to improve interdisciplinary reviews, defining key attributes of effective referee reports.Additionally, I’ll consider a shift towards a peer-witness reviewing model, questioning the conventional closed-door approach.
Gonzalo started his seminar titled Higher-order ghosts: spectral analysis of hypergraphs providing an overview of notions related to centrality measures in traditional networks, with a particular focus on spectral tools. Then, he introduced higher-order networks and hypergraphs.
How do we characterize the centrality of a node in hypergraphs? While this problem is technically challenging, Gonzalo reviewed the literature on this topic, addressing some of the current theoretical and practical limitations.
We then moved our discussion towards the state of peer review in academia. Gonzalo gave his perspective from an early career researcher working at the edge between multiple disciplines. Together, we brainstormed ways to foster a more accessible and open review system.
